论文标题
在广义的挖掘之和中
Vertex-Pancyclism in the Generalized Sum of Digraphs
论文作者
论文摘要
digraph $ d =（v（d）$，$ a（d）$的订单$ n \ geq 3 $是全盘的，只要$ d $包含一个定向$ k $的定向周期，每个$ k \ in \ in \ in \ in \ {3，\ ldots，\ ldots，n \} $; $ d $是v（d）$中的每个顶点$ v \ in \ {3，\ ldots，n \} $，$ d $的每个顶点$ v \ in vertex-pancyclic iff，$ d $，$ d $包含一个由$ v $传递的长度$ k $的周期。令$ d_1，d_2，\ ldots，d_k $为成对顶点脱节的集合。 $ d_1，d_2，\ ldots，d_k $的概括（g.s.），由$ \ oplus_ {i = 1}^k d_i $或$ d_1 \ oplus d_2 \ oplus d_2 \ oplus \ oplus \ cdots \ cdots \ oplus d_k $ $ v（d）= \ bigCup_ {i = 1}^k v（d_i）$，（ii）$ d \ langle v（d_i）\ rangle \ rangle \ cong d_i $ for $ i = 1,2，\ ldots，k $，k $和（iii）的每对属于$ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d的commands ar。 $ \ oplus_中的digraph $ d $ {i = 1}^k d_i $将被称为$ d_1，d_2，\ ldots，d_k $的广义总和（g.s.）。令$ d_1，d_2，\ ldots，d_k $为$ k $ pairwise顶点的集合，hamiltonian digraphs，在本文中，我们为digraph $ d \ in \ oplus_ {i = 1}^k d_i $ be degraph $ d \提供了足够的条件。该结果扩展了Cordero-Michel，Galeana-Sánchez和Goldfeder在2016年获得的结果。
A digraph $D=(V(D)$, $A(D))$ of order $n\geq 3$ is pancyclic, whenever $D$ contains a directed cycle of length $k$ for each $k\in \{3,\ldots,n\}$; and $D$ is vertex-pancyclic iff, for each vertex $v\in V(D)$ and each $k\in \{3,\ldots,n\}$, $D$ contains a directed cycle of length $k$ passing through $v$. Let $D_1, D_2, \ldots, D_k$ be a collection of pairwise vertex disjoint digraphs. The generalized sum (g.s.) of $D_1, D_2, \ldots, D_k$, denoted by $\oplus_{i=1}^k D_i$ or $D_1\oplus D_2 \oplus \cdots \oplus D_k$, is the set of all digraphs $D$ satisfying: (i) $V(D)=\bigcup_{i=1}^k V(D_i)$, (ii) $D\langle V(D_i) \rangle \cong D_i$ for $i=1,2,\ldots, k$, and (iii) for each pair of vertices belonging to different summands of $D$, there is exactly one arc between them, with an arbitrary but fixed direction. A digraph $D$ in $\oplus_{i=1}^k D_i$ will be called a generalized sum (g.s.) of $D_1, D_2, \ldots, D_k$. Let $D_1, D_2, \ldots, D_k$ be a collection of $k$ pairwise vertex disjoint Hamiltonian digraphs, in this paper we give simple sufficient conditions for a digraph $D\in \oplus_{i=1}^k D_i$ be vertex-pancyclic. This result extends a result obtained by Cordero-Michel, Galeana-Sánchez and Goldfeder in 2016.
